The signless Laplacian determination conjecture for multicone graphs

Let $K_r$ be the complete graph on $r$ vertices, let $sK_t$ be the disjoint union of $s$ copies of $K_t$, and let $K_r\triangledown sK_t$ denote their join. A graph is determined by its signless Laplacian spectrum (DQS) if every graph with the same signless Laplacian spectrum is isomorphic to it. Signless Laplacian determination conjecture for multicone graphs. Multicone graphs $K_r\triangledown sK_t$, except multicone graphs $K_r\bigtriangledown 3K_1$, are DQS. The paper notes that friendship graphs are known to be DQS and proposes this statement as a further conclusion; no resolution is supplied.